DOCSLIB.ORG

Short Run Supply Curve Is

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Short Run Supply Curve Is Review 1. Production function - Types of production functions - Marginal productivity - Returns to scale 2. The cost minimization problem - Solution: MPL(K,L)/w = MPK(K,L)/r - What happens when price of an input increases? 3. Deriving the cost function - Solution to cost minimization problem - Properties of the cost function (marginal and average costs) 1 Economic Profit Economic profit is the difference between total revenue and the economic costs. Difference between economic costs and accounting costs: The economic costs include the opportunity costs. Example: Suppose you start a business: - the expected revenue is $50,000 per year. - the total costs of supplies and labor are $35,000. - Instead of opening the business you can also work in the bank and earn $25,000 per year. - The opportunity costs are $25,000 - The economic profit is -$10,000 - The accounting profit is $15,000 2 Firm’s supply: how much to produce? A firm chooses Q to maximize profit. The firm’s problem max (Q) TR(Q) TC(Q) Q . Total cost of producing Q units depends on the production function and input costs. Total revenue of is the money that the firm receives from Q units (i.e., price times the quantity sold). It depends on competition and demand 3 Deriving the firm’s supply Def. A firm is a price taker if it can sell any quantity at a given price of p per unit. How much should a price taking firm produce? For a given price, the firm’s problem is to choose quantity to maximize profit. max pQTC(Q) Q s.t.Q 0 Optimality condition: P = MC(Q) Profit Maximization Optimality condition: 1. P = MC(Q) 2. MC(Q) increases Short Run Supply Example. A firm has the cost function TC(Q) = 100 + 20Q + Q2 and can sell each unit for a price of 30. How many units will it sell? What is the profit? . Calculate the firm’s profit if the market price is 40, 20, 15. Derive the firm’s supply. Short Run Supply A firm has the cost function TC(Q) = 100 + 20Q + Q2: . TFC = 100 $ SMC . ATC(Q)=100/Q+20+Q ATC . TVC(q) = 20Q + Q2 AVC . AVC(q) = 20 + Q . MC(q) = 20 + 2Q 20 ps Q The firm’s short run supply curve is: - If the price is P < 20: then the firm produces nothing Q = 0 푝−20 - If price is P > 20: then P = MC(Q) P = 20+2Q Q = 2 Short Run Supply 8 $ Supply SMC ATC AVC 2 ps 0 Q The firm’s short run supply curve is: - If the price is P < 20: then the firm produces nothing Q = 0 푝−20 - If price is P > 20: then P = MC(Q) P = 20+2Q Q = 2 The Firm’s Decision Does the firm choose to produce a positive quantity Q>0 or to shut down and produce nothing Q=0? 푝푠 = 푚푖푛푄퐴푉퐶(푄) Short Run Supply Key Definition: A single firm’s Short run supply curve specifies the profit maximizing output for each market price. The firm’s supply: If P < Ps, the firm produces nothing, Q=0 If P > Ps, the firm produces Q>0 such that MC(Q)=p $ Fixed costs are sunk: SMC ATC AVC Ps Quantity The Firm’s Decision The firm’s problem max (Q) TR(Q) TC(Q) Q Optimality condition: If MR(Q)> MC(Q), the firm’s profit increases if it produces more output. If MR(Q) < MC(Q), the firm’s profit decreases if it produces more output. The profit maximization condition is MR(Q) = MC(Q) . Since the firm is a price taker: p=MR(Q)=MC(Q) . We must also check the shut-down condition: p>MinAVC(Q) Short Run Supply Important to remember: if the firm produces output Q and sells it for a price p then: 1. When p>ATC(Q) the firm makes a profit. When p<ATC(Q) the firm loses money 2. When p>AVC(Q) the firm produces Q>0, when p<AVC(Q) the firm shuts down (assuming all fixed costs are sunk) 3. When AVC(Q)<p<ATC(Q) the firm operates at a loss Short Run Market Supply Curve Definition: The short run market supply is the sum of the quantities each firm supplies at that price. Example: suppose 3 types of firms with different marginal costs and different shut down prices Producer Surplus 14 The producer surplus is the monetary benefit of a producer p from a transaction= area between the supply curve and the price. Individual supply p* PS q* q Perfectly Competitive Market 15 A perfectly competitive market satisfies the following conditions: 1. Fragmented industry: consists of many small buyers and sellers. 2. Buyers and sellers are “price takers”: - Each buyer’s purchases are small and do not affect the market price. - Each seller is small and does not affect the market price. - No seller can affect the price of inputs. 3. Firms produce identical products. 4. Perfect information about prices. 5. All firms have equal access to inputs, have the same technology, and there is free entry. Implies that firms have identical long run cost functions. Perfectly Competitive Market 16 • The Law of One Price: Since products are identical and there is perfect information, there is a single price at which transactions occur. Why? What happens if one firm sets price p and another sets p’< p? • A single firm takes the price as given and chooses Q to maximize profit. max pQTC(Q) The firm’s problemQ s.t.Q 0 Optimal solution: p=MC(Q) Short Run Equilibrium 17 For a given number of firms N, a short run equilibrium is a pair of price and quantity (Q,P) such that: 1. Each producer maximizes profits given price P 2. Markets clear (aggregate supply equals aggregate demand) N S S D Q qi (P) Q (P) i1 푆 Where 푞푖 푃 is firm i’s individual profit-maximizing output given price P. Short Run Equilibrium Graphically Typical firm Market with n identical firms Supply $ $ SMC Supply ATC p* AVC ps Demand q* q Q*=nq* 18 Q Short Run Equilibrium: example 19 Suppose first that a market consists of 300 identical firms, all with the same cost curve: TC(q)= 0.1 + 150q2. Consumers’ demand is given by Qd(p) = 60 – p. (a) What is the equilibrium price and quantity? (b) Do firms make positive profits in the market equilibrium? Step 1: Derive individual supply curve FC = 0.1 (all are sunk, NSC= 0); AVC(q) = 150q; MC(q)=300q Since min{AVC(q)}=0, the firm always produces q>0. The profit maximizing condition: MC(q)=MR(q), we have that 300q=p, or qs(p) = p/300 Step 2: derive the market supply curve Qs(p) = 300 qs(p) =300(p/300) = p Step 3: solve for equilibrium Qs(p)= Qd(p) or p = 60 – p so that p1*= 30, Q* = 30 and each firm produces q1* = 30/300 = 0.1 Short Run Equilibrium: example 20 (b) Do firms make positive profits at the market equilibrium? Condition for positive profits: p* > ATC(q*) ATC (q)= TC(q)/q = 0.1/q + 150q. Since each firm produces q1* = 0.1, we have that ATC(q1*) = 16< 30 = p1*, Therefore, p1* > ATC(q1*) and profits are positive The profit of each firm is: pq-TC(q)= 30∙0.1-(0.1+150 ∙ 0.12)=1.4 Short Run Equilibrium: example 21 (c) What happens when the number of firms increases from 300 to 500? A single firm’s supply is unchanged: MC(q)=p and qs(p) = p/300 But now, market supply increases to Q(p)=500 (p/300) and for market to clear we have that: 500(p/300)= 60 – p or p2*=22.5 and Q2*= 37.5 and the individual firm produces q2* = 37.5/500 =0.075 (d) Does each firm earn a profit? Condition for positive profits: ATC(q*) < p* ATC (q2*)= 0.1/q + 150q= 0.1/0.075+150∙0.075 =12.58 < 22.5 = p2* The profit of each firm pq-TC(q)= 22.5 ∙ 0.075-(0.1+150 ∙ 0.0752)=0.7 Short Run Equilibrium: comparative statics 22 What happens when the number of firms increases? Market supply increases, price drops, and each firm produces less. Short Run Equilibrium: example 2 23 A town has 200 identical cafes, all with the same cost curve: TC(q)= FC+VC = 4 + 2q2. The inhabitants’ total demand for coffee is Qd(p) = 120 – 10 p. (a) What is the equilibrium price and quantity? (b) What is a single cafe’s profit? Calculate the town’s consumer, producer and total surpluses. (c) The town’s mayor closes 160 cafes in an effort to reduce the inhabitants’ coffee consumption. Answer (a) and (b) for n=40. How are the firms’ total profits and producer surplus related? Answers for n=200: p* = 2, Q* = 100, π = -3.5, CS = 500, PS = 100, TS = 600 Answers for n=40: p* = 6, Q* = 60, π = 0.5, CS = 180, PS = 180, TS = 360, PS = n (π+FC) = 40 (0.5+4) Short Run Equilibrium: producer surplus 24 p Producer surplus = area between the supply curve Demand and the price. Individual supply Profit = PS – FC (sunk) p* PS q* q Short Run Equilibrium: market surplus 25 p Suppose that all firms are identical (so linear supply). Demand CS Market supply In equilibrium on a perfectly competitive market, total surplus is maximized. p* PS Q* Q.
Load more

Recommended publications
  • Microeconomics Exam Review Chapters 8 Through 12, 16, 17 and 19
    MICROECONOMICS EXAM REVIEW CHAPTERS 8 THROUGH 12, 16, 17 AND 19 Key Terms and Concepts to Know CHAPTER 8 - PERFECT COMPETITION I. An Introduction to Perfect Competition A. Perfectly Competitive Market Structure: • Has many buyers and sellers. • Sells a commodity or standardized product. • Has buyers and sellers who are fully informed. • Has firms and resources that are freely mobile. • Perfectly competitive firm is a price taker; one firm has no control over price. B. Demand Under Perfect Competition: Horizontal line at the market price II. Short-Run Profit Maximization A. Total Revenue Minus Total Cost: The firm maximizes economic profit by finding the quantity at which total revenue exceeds total cost by the greatest amount. B. Marginal Revenue Equals Marginal Cost in Equilibrium • Marginal Revenue: The change in total revenue from selling another unit of output: • MR = ΔTR/Δq • In perfect competition, marginal revenue equals market price. • Market price = Marginal revenue = Average revenue • The firm increases output as long as marginal revenue exceeds marginal cost. • Golden rule of profit maximization. The firm maximizes profit by producing where marginal cost equals marginal revenue. C. Economic Profit in Short-Run: Because the marginal revenue curve is horizontal at the market price, it is also the firm’s demand curve. The firm can sell any quantity at this price. III. Minimizing Short-Run Losses The short run is defined as a period too short to allow existing firms to leave the industry. The following is a summary of short-run behavior: A. Fixed Costs and Minimizing Losses: If a firm shuts down, it must still pay fixed costs.
    [Show full text]
  • A Historical Sketch of Profit Theories in Mainstream Economics
    International Business Research; Vol. 9, No. 4; 2016 ISSN 1913-9004 E-ISSN 1913-9012 Published by Canadian Center of Science and Education A Historical Sketch of Profit Theories in Mainstream Economics Ibrahim Alloush Correspondence: Ibrahim Alloush ,Department of Economic Sciences, College of Economics and Administrative Sciences, Zaytouneh University, Amman, Jordan. Tel: 00962795511113, E-mail: [email protected] Received: January 4, 2016 Accepted: February 1, 2016 Online Published: March 16, 2016 doi:10.5539/ibr.v9n4p148 URL: http://dx.doi.org/10.5539/ibr.v9n4p148 Abstract In this paper, the main contributions to the development of profit theories are delineated in a chronological order to provide a quick reference guide for the concept of profit and its origins. Relevant theories are cited in reference to their authors and the school of thought they are affiliated with. Profit is traced through its Classical and Marginalist origins into its mainstream form in the literature of the Neo-classical school. As will be seen, the book is still not closed on a concept which may still afford further theoretical refinement. Keywords: profit theories, historical evolution of profit concepts, shares of income and marginal productivity, critiques of mainstream profit theories 1. Introduction Despite its commonplace prevalence since ancient times, “whence profit?” i.e., the question of where it comes from, has remained a vexing theoretical question for economists, with loaded political and moral implications, for many centuries. In this paper, the main contributions of different economists to the development of profit theories are delineated in a chronological order. The relevant theories are cited in reference to their authors and the school of thought they are affiliated with.
    [Show full text]
  • A Primer on Modern Monetary Theory
    2021 A Primer on Modern Monetary Theory Steven Globerman fraserinstitute.org Contents Executive Summary / i 1. Introducing Modern Monetary Theory / 1 2. Implementing MMT / 4 3. Has Canada Adopted MMT? / 10 4. Proposed Economic and Social Justifications for MMT / 17 5. MMT and Inflation / 23 Concluding Comments / 27 References / 29 About the author / 33 Acknowledgments / 33 Publishing information / 34 Supporting the Fraser Institute / 35 Purpose, funding, and independence / 35 About the Fraser Institute / 36 Editorial Advisory Board / 37 fraserinstitute.org fraserinstitute.org Executive Summary Modern Monetary Theory (MMT) is a policy model for funding govern- ment spending. While MMT is not new, it has recently received wide- spread attention, particularly as government spending has increased dramatically in response to the ongoing COVID-19 crisis and concerns grow about how to pay for this increased spending. The essential message of MMT is that there is no financial constraint on government spending as long as a country is a sovereign issuer of cur- rency and does not tie the value of its currency to another currency. Both Canada and the US are examples of countries that are sovereign issuers of currency. In principle, being a sovereign issuer of currency endows the government with the ability to borrow money from the country’s cen- tral bank. The central bank can effectively credit the government’s bank account at the central bank for an unlimited amount of money without either charging the government interest or, indeed, demanding repayment of the government bonds the central bank has acquired. In 2020, the cen- tral banks in both Canada and the US bought a disproportionately large share of government bonds compared to previous years, which has led some observers to argue that the governments of Canada and the United States are practicing MMT.
    [Show full text]
  • Modern Monetary Theory: Cautionary Tales from Latin America
    Modern Monetary Theory: Cautionary Tales from Latin America Sebastian Edwards* Economics Working Paper 19106 HOOVER INSTITUTION 434 GALVEZ MALL STANFORD UNIVERSITY STANFORD, CA 94305-6010 April 25, 2019 According to Modern Monetary Theory (MMT) it is possible to use expansive monetary policy – money creation by the central bank (i.e. the Federal Reserve) – to finance large fiscal deficits that will ensure full employment and good jobs for everyone, through a “jobs guarantee” program. In this paper I analyze some of Latin America’s historical episodes with MMT-type policies (Chile, Peru. Argentina, and Venezuela). The analysis uses the framework developed by Dornbusch and Edwards (1990, 1991) for studying macroeconomic populism. The four experiments studied in this paper ended up badly, with runaway inflation, huge currency devaluations, and precipitous real wage declines. These experiences offer a cautionary tale for MMT enthusiasts.† JEL Nos: E12, E42, E61, F31 Keywords: Modern Monetary Theory, central bank, inflation, Latin America, hyperinflation The Hoover Institution Economics Working Paper Series allows authors to distribute research for discussion and comment among other researchers. Working papers reflect the views of the author and not the views of the Hoover Institution. * Henry Ford II Distinguished Professor, Anderson Graduate School of Management, UCLA † I have benefited from discussions with Ed Leamer, José De Gregorio, Scott Sumner, and Alejandra Cox. I thank Doug Irwin and John Taylor for their support. 1 1. Introduction During the last few years an apparently new and revolutionary idea has emerged in economic policy circles in the United States: Modern Monetary Theory (MMT). The central tenet of this view is that it is possible to use expansive monetary policy – money creation by the central bank (i.e.
    [Show full text]
  • Modern Monetary Theory: a Marxist Critique
    Class, Race and Corporate Power Volume 7 Issue 1 Article 1 2019 Modern Monetary Theory: A Marxist Critique Michael Roberts [email protected] Follow this and additional works at: https://digitalcommons.fiu.edu/classracecorporatepower Part of the Economics Commons Recommended Citation Roberts, Michael (2019) "Modern Monetary Theory: A Marxist Critique," Class, Race and Corporate Power: Vol. 7 : Iss. 1 , Article 1. DOI: 10.25148/CRCP.7.1.008316 Available at: https://digitalcommons.fiu.edu/classracecorporatepower/vol7/iss1/1 This work is brought to you for free and open access by the College of Arts, Sciences & Education at FIU Digital Commons. It has been accepted for inclusion in Class, Race and Corporate Power by an authorized administrator of FIU Digital Commons. For more information, please contact [email protected]. Modern Monetary Theory: A Marxist Critique Abstract Compiled from a series of blog posts which can be found at "The Next Recession." Modern monetary theory (MMT) has become flavor of the time among many leftist economic views in recent years. MMT has some traction in the left as it appears to offer theoretical support for policies of fiscal spending funded yb central bank money and running up budget deficits and public debt without earf of crises – and thus backing policies of government spending on infrastructure projects, job creation and industry in direct contrast to neoliberal mainstream policies of austerity and minimal government intervention. Here I will offer my view on the worth of MMT and its policy implications for the labor movement. First, I’ll try and give broad outline to bring out the similarities and difference with Marx’s monetary theory.
    [Show full text]
  • Reading and Understanding Nonprofit Financial Statements
    Reading and Understanding Nonprofit Financial Statements What does it mean to be a nonprofit? • A nonprofit is an organization that uses surplus revenues to achieve its goals rather than distributing them as profit or dividends. • The mission of the organization is the main goal, however profits are key to the growth and longevity of the organization. Your Role in Financial Oversight • Ensure that resources are used to accomplish the mission • Ensure financial health and that contributions are used in accordance with donor intent • Review financial statements • Compare financial statements to budget • Engage independent auditors Cash Basis vs. Accrual Basis • Cash Basis ▫ Revenues and expenses are not recognized until money is exchanged. • Accrual Basis ▫ Revenues and expenses are recognized when an obligation is made. Unaudited vs. Audited • Unaudited ▫ Usually Cash Basis ▫ Prepared internally or through a bookkeeper/accountant ▫ Prepared more frequently (Quarterly or Monthly) • Audited ▫ Accrual Basis ▫ Prepared by a CPA ▫ Prepared yearly ▫ Have an Auditor’s Opinion Financial Statements • Statement of Activities = Income Statement = Profit (Loss) ▫ Measures the revenues against the expenses ▫ Revenues – Expenses = Change in Net Assets = Profit (Loss) • Statement of Financial Position = Balance Sheet ▫ Measures the assets against the liabilities and net assets ▫ Assets = Liabilities + Net Assets • Statement of Cash Flows ▫ Measures the changes in cash Statement of Activities (Unaudited Cash Basis) • Revenues ▫ Service revenues ▫ Contributions
    [Show full text]
  • Principles of Microeconomics
    PRINCIPLES OF MICROECONOMICS A. Competition The basic motivation to produce in a market economy is the expectation of income, which will generate profits. • The returns to the efforts of a business - the difference between its total revenues and its total costs - are profits. Thus, questions of revenues and costs are key in an analysis of the profit motive. • Other motivations include nonprofit incentives such as social status, the need to feel important, the desire for recognition, and the retaining of one's job. Economists' calculations of profits are different from those used by businesses in their accounting systems. Economic profit = total revenue - total economic cost • Total economic cost includes the value of all inputs used in production. • Normal profit is an economic cost since it occurs when economic profit is zero. It represents the opportunity cost of labor and capital contributed to the production process by the producer. • Accounting profits are computed only on the basis of explicit costs, including labor and capital. Since they do not take "normal profits" into consideration, they overstate true profits. Economic profits reward entrepreneurship. They are a payment to discovering new and better methods of production, taking above-average risks, and producing something that society desires. The ability of each firm to generate profits is limited by the structure of the industry in which the firm is engaged. The firms in a competitive market are price takers. • None has any market power - the ability to control the market price of the product it sells. • A firm's individual supply curve is a very small - and inconsequential - part of market supply.
    [Show full text]
  • PRINCIPLES of MICROECONOMICS 2E
    PRINCIPLES OF MICROECONOMICS 2e Chapter 8 Perfect Competition PowerPoint Image Slideshow Competition in Farming Depending upon the competition and prices offered, a wheat farmer may choose to grow a different crop. (Credit: modification of work by Daniel X. O'Neil/Flickr Creative Commons) 8.1 Perfect Competition and Why It Matters ● Market structure - the conditions in an industry, such as number of sellers, how easy or difficult it is for a new firm to enter, and the type of products that are sold. ● Perfect competition - each firm faces many competitors that sell identical products. • 4 criteria: • many firms produce identical products, • many buyers and many sellers are available, • sellers and buyers have all relevant information to make rational decisions, • firms can enter and leave the market without any restrictions. ● Price taker - a firm in a perfectly competitive market that must take the prevailing market price as given. 8.2 How Perfectly Competitive Firms Make Output Decisions ● A perfectly competitive firm has only one major decision to make - what quantity to produce? ● A perfectly competitive firm must accept the price for its output as determined by the product’s market demand and supply. ● The maximum profit will occur at the quantity where the difference between total revenue and total cost is largest. Total Cost and Total Revenue at a Raspberry Farm ● Total revenue for a perfectly competitive firm is a straight line sloping up; the slope is equal to the price of the good. ● Total cost also slopes up, but with some curvature. ● At higher levels of output, total cost begins to slope upward more steeply because of diminishing marginal returns.
    [Show full text]
  • Opportunity Cost and Explain Why Accounting Profits and Economic Profits Are Not the Same.”
    Microeconomics Topic 1: “Explain the concept of opportunity cost and explain why accounting profits and economic profits are not the same.” Reference: Gregory Mankiw’s Principles of Microeconomics, 2nd edition, Chapter 1 (p. 3-6) and Chapter 13 (p. 270-2). Scarcity Economics is the study of how people make choices under scarcity. What is scarcity? Scarcity means that resources are limited. There are not enough resources available to satisfy everyone’s wants. This is clearly true for individuals. Your income is limited. You cannot buy everything you want, so you must choose between different alternatives. Your time is also limited. You cannot do everything you want to, so you are forced to choose between different alternatives. If you choose to spend the day at the beach, you give up going to class or working. Opportunity Cost This concept of scarcity leads to the idea of opportunity cost. The opportunity cost of an action is what you must give up when you make that choice. Another way to say this is: it is the value of the next best opportunity. Opportunity cost is a direct implication of scarcity. People have to choose between different alternatives when deciding how to spend their money and their time. Milton Friedman, who won the Nobel Prize for Economics, is fond of saying "there is no such thing as a free lunch." What that means is that in a world of scarcity, everything has an opportunity cost. There is always a trade-off involved in any decision you make. The concept of opportunity cost is one of the most important ideas in economics.
    [Show full text]
  • The Spectre of Monetarism
    The Spectre of Monetarism Speech given by Mark Carney Governor of the Bank of England Roscoe Lecture Liverpool John Moores University 5 December 2016 I am grateful to Ben Nelson and Iain de Weymarn for their assistance in preparing these remarks, and to Phil Bunn, Daniel Durling, Alastair Firrell, Jennifer Nemeth, Alice Owen, James Oxley, Claire Chambers, Alice Pugh, Paul Robinson, Carlos Van Hombeeck, and Chris Yeates for background analysis and research. 1 All speeches are available online at www.bankofengland.co.uk/publications/Pages/speeches/default.aspx Real incomes falling for a decade. The legacy of a searing financial crisis weighing on confidence and growth. The very nature of work disrupted by a technological revolution. This was the middle of the 19th century. Liverpool was in the midst of a golden age; its Custom House was the national Exchequer’s biggest source of revenue. And Karl Marx was scribbling in the British Library, warning of a spectre haunting Europe, the spectre of communism. We meet today during the first lost decade since the 1860s. In the wake of a global financial crisis. And in the midst of a technological revolution that is once again changing the nature of work. Substitute Northern Rock for Overend Gurney; Uber and machine learning for the Spinning Jenny and the steam engine; and Twitter for the telegraph; and you have dynamics that echo those of 150 years ago. Then the villains were the capitalists. Should they today be the central bankers? Are their flights of fancy promoting stagnation and inequality? Does the spectre of monetarism haunt our economies?i These are serious charges, based on real anxieties.
    [Show full text]
  • Profit Maximization
    PROFIT MAXIMIZATION [See Chap 11] 1 Profit Maximization • A profit-maximizing firm chooses both its inputs and its outputs with the goal of achieving maximum economic profits 2 Model • Firm has inputs (z 1,z 2). Prices (r 1,r 2). – Price taker on input market. • Firm has output q=f(z 1,z 2). Price p. – Price taker in output market. • Firm’s problem: – Choose output q and inputs (z 1,z 2) to maximise profits. Where: π = pq - r1z1 – r2z2 3 1 One-Step Solution • Choose (z 1,z 2) to maximise π = pf(z 1,z 2) - r1z1 – r2z2 • This is unconstrained maximization problem. • FOCs are ∂ ( , ) ∂ ( , ) f z1 z2 = f z1 z2 = p r1 and p r2 z1 z2 • Together these yield optimal inputs zi*(p,r 1,r 2). • Output is q*(p,r 1,r 2) = f(z 1*, z2*). This is usually called the supply function. π • Profit is (p,r1,r 2) = pq* - r1z1* - r2z2* 4 1/3 1/3 Example: f(z 1,z 2)=z 1 z2 π 1/3 1/3 • Profit is = pz 1 z2 - r1z1 – r2z2 • FOCs are 1 1 pz − 3/2 z 3/1 = r and pz 3/1 z − 3/2 = r 3 1 2 1 3 1 2 2 • Solving these two eqns, optimal inputs are 3 3 * = 1 p * = 1 p z1 ( p,r1,r2 ) 2 and z2 ( p,r1, r2 ) 2 27 r1 r2 27 1rr 2 • Optimal output 2 * = * 3/1 * 3/1 = 1 p q ( p, r1,r2 ) (z1 ) (z2 ) 9 1rr 2 • Profits 3 π * = * − * − * = 1 p ( p, r1,r2 ) pq 1zr 1 r2 z2 27 1rr 2 5 Two-Step Solution Step 1: Find cheapest way to obtain output q.
    [Show full text]
  • 13. Chartalism, Metallism, and Key Currencies
    13. Chartalism, Metallism, and Key Currencies In terms of our hierarchy of money and credit, we have so far been paying most attention to currency and everything below it, so our attention has been on two of the four prices of money, namely par and the interest rate. Today we begin a section of the course that looks into forms of money that lie above currency in the hierarchy, and hence at a third price of money, the rate of exchange. Metallism Under a gold standard, the extension of our analysis would be straightforward. Gold is the ultimate international money, an asset that is no one’s liability. Under a gold standard, each currency has its own mint par, and the exchange rate is determined by the ratio of mint pars. In this view of the world, the multiple national (state) systems relate to one another not directly (money to money) but only indirectly (credit to credit) through the international (private) system. Each national currency has an exchange rate with the international money and it is that pattern of exchange rates that sets up a pattern of exchange rates between national currencies. Dollar = x ounces of gold Pound = y ounces of gold Dollar = x/y Pounds [S(1/x)=(1/y)] Exchange Rate in a Metallic Standard World Gold X oz. Y oz. Dollar S=X/Y Pound Deposits Deposits Securities Securities From this point of view, the central bank is a banker’s bank, holding international reserves that keep the national payment system in more or less connection with the international system.
    [Show full text]